Talk:Rated voting

Impossibility theorems
"Others, however, argue that this is not true, for instance because interpersonal comparisons of cardinal measures are impossible."

1. What does this have to do with Arrow's impossibility theorem not applying to range ballots?

2. Anyway, it's preferential ballots that are not interpersonally comparable, because they destroy information about distance. All these ballots:

A                          B C D A B C                           D A      B      C        D A              B  C             D

are compressed into an equally spaced ballot of A > B > C > D.

"In any case, cardinal systems do fall under the Gibbard–Satterthwaite theorem, and therefore any such system must be subject to strategic voting in some instances."

I've heard that the theorem only applies to ranked systems, but also that it doesn't matter because range systems can be re-interpreted as ranked systems and fail the theorem. Which is correct? 71.167.61.127 (talk) 17:01, 10 December 2016 (UTC)


 * Well obviously strategic voting would be an issue in cardinal voting systems, whether or not we say the GS theorem applies. If a candidate is your least favorite among the realistic candidates, you will always decrease the chance that he is elected by giving him the lowest possible rating and that would be the strategic thing to do, even if you actually think he would be okay. MathHisSci (talk) —Preceding undated comment added 11:22, 8 April 2017 (UTC)

Merge proposal
It does seem that a Ratings ballot and Cardinal voting have such a similar scope that they are best described on the same page. Klbrain (talk) 22:47, 25 July 2018 (UTC)
 * ✅ Klbrain (talk) 21:59, 12 August 2018 (UTC)

Disapproval voting and negative assignment
I don't know what this paragraph means, so I'm moving it to talk page:

"Other variants include disapproval voting options such as negative assignment, but typically out of the same absolute number of votes. That is, a -2 and a +8 add up to ten points, not six, because the absolute value of a negative vote is the same as positive."

It was added by an IP here: https://en.wikipedia.org/w/index.php?title=Cardinal_voting&diff=prev&oldid=633428976&diffmode=source

Cumulative voting seems to be a cardinal voting system
I'm not sure why Cumulative voting isn't mentioned in this article. A sentence in the Cumulative voting article says "Unlike choice voting where the numbers represent the order of a voter's ranking of candidates (i.e. they are ordinal numbers), in cumulative votes the numbers represent quantities (i.e. they are cardinal numbers)"... -- AnonMoos (talk) 00:50, 7 June 2019 (UTC)


 * @AnonMoos I would very much like to resolve this fundamental conflict of terms. My understanding of social choice theory, game theory and mathematics is amateur, and my short literature search didn't bring up any conclusive source: I need help! I just signed up to the | electorama election-methods mailing list to ask there, but my application is still pending.
 * As you said, this article claims cardinal voting "allows the voter to give each candidate an independent evaluation". This definition excludes cumulative voting, and by extension quadratic voting, which provide each voter with a balance of points they can allocate between the options as they please.
 * However, cumulative voting claims to be "a multiple-winner cardinal voting method", on the basis that "in cumulative votes the numbers represent quantities (i.e. they are cardinal numbers)." Further, quadratic voting claims to be "a variant of cumulative voting in the class of cardinal voting."
 * Based on what I understand of cardinality and cardinal numbers, I tend to believe that this article is in error, and that the definition should read something like "Cardinal voting refers to any voting method where the votes are cardinal numbers indicating definite quantities (e.g. 1, 7, 0, -1)."
 * Pinging people from mentioned pages who may have useful opinions on the topic:
 * Cheers, DougInAMug talk 13:34, 21 May 2022 (UTC)
 * Seems like editors ended in the right place. Cumulative voting for sure is not a cardinal voting method, as there are set number of votes and for that reason the voter cannot independent evaluate each candidates RRichie (talk) 21:14, 24 June 2023 (UTC)


 * Cumulative voting seems to be mischaracterized, edit October 31, 2019 by AnonMoos, with comment Talk:Cumulative_voting. That should be removed. Tom Ruen (talk) 23:33, 21 May 2022 (UTC)
 * @Tomruen I did a moderate literature review, and could find no definition of cardinal voting that clearly includes cumulative voting. Until a referenced source to the contrary is found, I agree with you that cumulative voting and quadratic voting should not make the claim to be cardinal, since that would be original research. I would make those changes in some days, unless you/someone else gets there first.
 * If cumulative voting is neither ordinal nor cardinal though, where does it lie? Is it itself a third class? A question perhaps better on the respective page at a later point. DougInAMug talk 22:24, 22 May 2022 (UTC)
 * Cumulative voting fits as a "single vote" system. Ranked ballots or not is kind of irrelevant. Single transferable vote can be seen as an optimized cumulative voting where a single fractional vote is distributed among 1 or more candidates to maximize how many winners it helps influence. Tom Ruen (talk) 07:37, 23 May 2022 (UTC)
 * For instance Equal & Even cumulative voting is a variation with an "approval ballot", where you can only vote for a candidate or not, and your fractional vote is divided equally among your chosen set of candidates. Tom Ruen (talk) 07:40, 23 May 2022 (UTC)
 * I like this table Bullet_voting presentation, showing a progression of single non-transferable vote, Instant runoff voting (STV without surplus transfer), Cumulative voting, Single transferable vote, as single vote systems. Limited voting, Plurality-at-large voting, Approval voting, Range voting, and Borda voting are multivote systems which may allow a majority to control all/most of the winners. Tom Ruen (talk) 07:47, 23 May 2022 (UTC)
 * @Tomruen Thanks for those points. This '3rd category', "single vote methods" doesn't seem to be recognised anywhere. I feel like 'currency' or 'point' most accurately describes the difference from 'ranking' and 'scoring' methods. In any case, without a reliable source for categorization, cumulative and 'single vote' methods should remain independent. DougInAMug talk 15:57, 26 May 2022 (UTC)

Sorry for the delay. I would consider cumulative voting to be in its own class, not cardinal. — Omegatron (talk) 19:52, 24 September 2022 (UTC)

"In any case, cardinal methods do fall under Gibbard's theorem, and therefore any such method must be subject to strategic voting in some instances."
Is there a single voting system that is not subject to strategic voting in some instances? What purpose does this sentence serve? Primecut (talk) 03:51, 10 August 2019 (UTC)

"The opposite is not true: Rankings cannot be converted to ratings, since ratings carry more information about strength of preference, which is destroyed when converting to rankings. "
I can trivially convert rankings to ratings. 1. Candidate A, 2. Candidate B, 3. Candidate C --> Candidate A: 3, Candidate B: 2, Candidate C: 1. Boom, I did it. Unsourced and clearly false statement btfo 69.113.166.178 (talk) 22:44, 5 July 2021 (UTC)


 * Yuup, this clearly needs to be removed or rephrased or properly sourced. 141.136.205.25 (talk) 18:01, 4 May 2024 (UTC)

Renaming of Page
I am not too sure if "Rated Voting" is a better page title than "Cardinal Voting". Rated Voting as a name does not really seem to be used in the literature. Jannikp97 (talk) 02:49, 28 February 2024 (UTC)


 * @Closed Limelike Curves I still believe that btw, have never heard any other social choice people use "rated voting" instead of "cardinal voting" Jannikp97 (talk) 07:40, 4 May 2024 (UTC)
 * Hi, sorry I missed this! I've seen both used in academic papers or literature. I think "Cardinal voting" is more popular in academic contexts, but went with "rated" because 1) it fits more closely with ranked voting and 2) it's a less-confusing word for the average person. Closed Limelike Curves (talk) 02:51, 20 July 2024 (UTC)

Real-world examples?
Even if the sub-articles or sub-sub-articles have some examples of real-world political (national, local, supranational) systems where rated voting systems are used, it would be good to have a few of these listed in this article. This article looks currently like it only presents mathematical/statistical arguments of systems that should be used, but have not (yet?) been used.

If these systems are in use, it would be good to mention a few of these in this article, with WP:RS, of course. Boud (talk) 11:39, 4 May 2024 (UTC)


 * Hi,
 * I think I would agree that this would be nice. For approval voting there seems to be some adoption listed in its article. For score voting aswell, however, the listed adoptions there seem to be mostly unsourced. Jannikp97 (talk) 15:28, 4 May 2024 (UTC)
 * These systems are about as widely-used as ranked voting. Approval voting has been adopted in a few US cities as well as Latvia. Majority Judgment is used in France for party primaries.
 * https://link.springer.com/article/10.1007/s10602-022-09385-7 Closed Limelike Curves (talk) 21:35, 16 July 2024 (UTC)

Ranked voting is a nice 'Adoption' section. Boud (talk) 11:42, 4 May 2024 (UTC)